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Let X and Y be two independent exponential random variables. Denote X as the time until...

Let X and Y be two independent exponential random variables. Denote X as the time until Bob comes with average waiting time 1/lamda (lambda > 0). Denote Y as the time until Gary comes with average waiting time 1/mu (mu >0). Let S be the time before both of them come.
a) What is the distribution of S?
b) Derive the probability mass function of T defined by T=0 if Bob comes first and T=1 if Gary comes first.
c) Are S and T independent?

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